where \(\textrm {v}_S\)  is the VEV of the scalar singlet (designated by \(\xi \)  in Ref. [1]}) that is needed to break the \(U(1)^\prime \)  symmetry and \(c_h=\cos \theta _h,s_h=\sin \theta _h\)  are the cosine and sine of the mixing angle:
\(\left( \begin{array}{c}\phi _{SM}\\ \phi _H\end{array}\right)=\left(\begin{array}{cc}c_h & s_h\\-s_h &c_h\end{array}\right)\left(\begin{array}{c}h \\H\end{array}\right).\) 
